Algebra Seminar: Webs and pockets in SL(4) affine building

Haihan Wu, University of Virginia

Title: Webs and pockets in SL(4) affine building

Abstract: To study the representation theory of quantum SL(2) diagrammatically, one can study the Temperley-Lieb category, whose basis morphisms are planar matchings. A generalization to the SL(3) case gives rise to the SL(3) web category, whose basis morphisms are given by non-elliptic webs - planar trivalent graphs with girth greater or equal to 6. It is shown by Fontaine-Kamnitzer-Kuperberg that the dual graphs of SL(3) basis webs are embedded isometrically into the SL(3) affine building, which is defined as a simplicial complex with vertices given by elements in the affine Grassmannian. In this talk, I will review background material and talk about a generalization of the embeddings to the SL(4) case, based on joint work in progress with Gaetz-Striker-Swanson.